What kind of things is your party interested in? Famous monuments and museums? Nightlife? Neighborhoods? Getting off the beaten track? Wine tasting? Shopping? Paris has a ton of things to offer, so it's good to know what you are after. Here is a basic Paris itinerary that sees the main sights and is very busy- you can modify it to your tastes:

Day 1: Arrive in Paris, check into your accommodation, pick a nearby place for dinner. Explore the area around where you're staying by foot to get familiar with it.

I think that to truly appreciate and allow Paris to become a part of you,

You definitely need more time. The City of Light is also small enough to to visit it and understand where you'd love to devote your time to in the future with your 4 day/ 3 night timeline. I would hire a walking tour like www.parisfootwalks.com and allow them to show you in an organized time efficient manner the layout of the city whilst sightseeing and covering some of the main monuments you must see.

As far as restaurants go, I would most definitely go for breakfast at Angélinaon Rue de Rivoli. Restaurant recommendations will be highly influenced on the neighborhood you stay at. Personally, I like to discover on my own and away from touristy areas. Breakfast is a 'thing' in Paris but simple at the same time. A 'petit déjeuner' is something to do. I also think that keeping the last day free would be helpful so that you can go back to an area you didn't spend enough time in or it could be a fun shopping day.

You have lots of touristic places along the main Quai de la Seine, so if you take a walk you can check them all (this only if you don't want to visit them, if so check online to see if you can buy in advance or if you can schedule yourself otherwise get prepared to stay in very long queues)

You really can't cover Paris in 3-4 days. I've been there repeatedly and have only scratched the surface!

Crystal gave you some good info. I would add - if you will be there on a Sunday, head to the Marais. The stores and restaurants are open, unlike in other areas. Don't miss Place des Vosges, one of the most beautiful parks in Paris. If you're in the area on a Thursday or Sunday, one of the best markets is by the Bastille - also known as Richard-Lenoir. Great foods for a picnic at Place des Vosges. Or from here you can head up to Canal Saint-Martin - lots of great shopping and restaurants (Hôtel du Nord and Chez Prune are very popular).

I would also add Ile Saint-Louis to Crystal's itinerary after Notre Dame. It's a little touristy but beautiful. It is also great at night - you can sit at one of the cafes facing Notre Dame after strolling around.

If you want to have lunch after Notre Dame, head to the point of the island - to Place Dauphine - a gorgeous square lined with restaurants. My favorite is Rose of France.

I wouldnt go all the way to Versailles on a first trip when you have such limited time, unless this is a huge priority. It was about my 10th trip before I went.

Another idea is a Seine cruise - either in the evening or during the day. In the evening they will sit in front of the Eiffel Tower, so you can get good photos of the lights. I agree - visit the Eiffel Tower at night to maximize your day time.

Google Patrick Blanc Vertical Gardens. There's a gorgeous one at the top of Rue Montorgueil which is a great shopping street very close to the best cookware stores like Dehillerinif you like that sort of stuff.